This paper proposes to characterize the fingerprint orientation using a novel topological representation, which transforms the orientation field into a map composed of a set of geometric objects and analyzes the properties of each geometric object based on two assumptions: regional coherence assumption and convexity assumption. Different from prior works on fingerprint orientation analysis, this approach has a capability to identify where the errors happen, not only the “random errors” (which is assumed by local-filtering and global modeling methods), but also the “structure irregularities”, which often occur in real prints and impose difficulty on existing techniques.